A Statistical-Mechanical Approach To Generalized Statistics of Quantum and Classical Gases

For many particle non-interacting gases which are in heat and particle baths the grand canonical ensemble concept has been set out. The set of occupation numbers of the R quantum states of the gas is described by {n(1), n(2),..., n(k),...}. As the entropy of the ensemble, one of the fractal inspired entropies, namely T sallis entropy, has been considered and expressed for the ensemble. The probability P-R of the ensemble to be in the slate R has been investigated for the equilibrium state, by making use of the Boltzmann H-theorem with the techniques of calculus of variations. Having obtained the probability P-R, the generalized distribution functions of the quantum gases have been established. On the other hand, the generalized distribution functions of the classical gases have been found as a special case of one of the quantum gases, namely the boson gas.